Every connected sum of lens spaces is a real component of a uniruled algebraic variety

Johannes Huisman[1]; Frédéric Mangolte[2]

  • [1] Université de Bretagne Occidentale, Département de Mathématiques, CNRS UMR 6205, 6 avenue Victor Le Gorgeu, CS 93837, 29238 Brest cedex 3 (France)
  • [2] Université de Savoie, Laboratoire de Mathématiques, 73376 Le Bourget du Lac Cedex (France)

Annales de l'institut Fourier (2005)

  • Volume: 55, Issue: 7, page 2475-2487
  • ISSN: 0373-0956

Abstract

top
We show that any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled projective variety, and prove a conjecture of János Kollár.

How to cite

top

Huisman, Johannes, and Mangolte, Frédéric. "Every connected sum of lens spaces is a real component of a uniruled algebraic variety." Annales de l'institut Fourier 55.7 (2005): 2475-2487. <http://eudml.org/doc/116260>.

@article{Huisman2005,
abstract = {We show that any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled projective variety, and prove a conjecture of János Kollár.},
affiliation = {Université de Bretagne Occidentale, Département de Mathématiques, CNRS UMR 6205, 6 avenue Victor Le Gorgeu, CS 93837, 29238 Brest cedex 3 (France); Université de Savoie, Laboratoire de Mathématiques, 73376 Le Bourget du Lac Cedex (France)},
author = {Huisman, Johannes, Mangolte, Frédéric},
journal = {Annales de l'institut Fourier},
keywords = {Uniruled algebraic variety; Seifert fibered manifold; lens space; connected sum; equivariant line bundle; real algebraic model; Seifert fibred manifold; real algebraic},
language = {eng},
number = {7},
pages = {2475-2487},
publisher = {Association des Annales de l'Institut Fourier},
title = {Every connected sum of lens spaces is a real component of a uniruled algebraic variety},
url = {http://eudml.org/doc/116260},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Huisman, Johannes
AU - Mangolte, Frédéric
TI - Every connected sum of lens spaces is a real component of a uniruled algebraic variety
JO - Annales de l'institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 7
SP - 2475
EP - 2487
AB - We show that any finite connected sum of lens spaces is diffeomorphic to a real component of a uniruled projective variety, and prove a conjecture of János Kollár.
LA - eng
KW - Uniruled algebraic variety; Seifert fibered manifold; lens space; connected sum; equivariant line bundle; real algebraic model; Seifert fibred manifold; real algebraic
UR - http://eudml.org/doc/116260
ER -

References

top
  1. A. Comessatti, Sulla connessione delle superfizie razionali reali, Annali di Math. 23 (1914), 215-283 Zbl45.0889.02
  2. K.H. Dovermann, M. Masuda, D.Y. Suh, Algebraic realization of equivariant vector bundles, J. reine angew. Math. 448 (1994), 31-64 Zbl0787.57016MR1266746
  3. J. Huisman, F. Mangolte, Every orientable Seifert 3-manifold is a real component of a uniruled algebraic variety, Topology 44 (2005), 63-71 Zbl1108.14048MR2104001
  4. V. Kharlamov, Variétés de Fano réelles (d'après C. Viterbo), Séminaire Bourbaki 872 (1999/2000) Zbl1004.53059
  5. J. Kollár, The Nash conjecture for threefolds, ERA of Amer. Math. Soc. 4 (1998), 63-73 Zbl0896.14030MR1641168
  6. J. Kollár, Real algebraic threefolds. II. Minimal model program, J. Amer. Math. Soc. 12 (1999), 33-83 Zbl0964.14013MR1639616
  7. J. Kollár, Real algebraic, J. Math. Sci., New York 94 (1999), 996-1020 Zbl0964.14014MR1703903
  8. J. Kollár, The topology of real and complex algebraic varieties, Adv. Stud. Pure Math. (2001) Zbl1036.14010MR1865090
  9. Y. Miyaoka, On the Kodaira dimension of a minimal threefold, Math. Ann. 281 (1988), 325-332 Zbl0625.14023MR949837
  10. S. Mori, Flip theorem and the existence of minimal models for threefolds, J. Amer. Math. Soc. 1 (1988), 117-253 Zbl0649.14023MR924704
  11. J. Nash, Real algebraic manifolds, Ann. Math. 56 (1952), 405-421 Zbl0048.38501MR50928
  12. P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401-487 Zbl0561.57001MR705527

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.